Travelling wave solutions to the K-P-P equation: alternatives to Simon Harris' probabilistic analysis

By Andreas E. Kyprianou. 2004

101 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Condensed Matter Physics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4c6c28dcd2ebeef357f12248bf18d00e666704ac

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Elie Aidékon
2. Zhan Shi
3. S. Harris
4. J. Harris
5. Élie Aïdékon
6. J. Berestycki
7. E. Brunet
8. Andreas E. Kyprianou

In Condensed Matter Physics

1. Elie Aidékon
2. Zhan Shi
3. S. Harris
4. J. Harris
5. Élie Aïdékon
6. J. Berestycki
7. E. Brunet
8. Andreas E. Kyprianou

In Mathematical Physics

1. Zhan Shi
2. Elie Aidékon
3. S. Harris
4. Thomas Madaule
5. J. Harris
6. Élie Aïdékon
7. J. Berestycki
8. E. Brunet

Citations in the corpus

• Survival probabilities for branching Brownian motion with absorption (2007, methodology): “For full details of the construction of such changes of measure we refer the reader to the spine theory given in Hardy and Harris [11], but also see Chauvin and Rouault [6], and Kyprianou [18].”
• Convergence in law of the minimum of a branching random walk (2013, background): “The analog in the case of the Brownian motion is Theorem 9 in [20].”
• Branching random walks (2015, background): “Most of the material in this chapter can be found in Biggins and Kyprianou [58].”
• The Seneta–Heyde scaling for the branching random walk (2011, methodology): “The truncation argument can be traced back to Harris [17]; we use it in the context of conditional spines, following the formalism of Kyprianou [23].”
• Convergence in law of the minimum of a branching random walk (2011, background): “The analog in the case of the Brownian motion is Theorem 9 in [20].”
• A simple path to asymptotics for the frontier of a branching Brownian motion (2011, unknown): “This function u satisfies the Fisher–Kolmogorov–Petrovski–Piscounov equation ut = 12uxx + u2 − u (with Heaviside initial condition), which has been studied for many years both analytically and probabilistically; see, for example, Kolmogorov et al. [13], Fisher [6], Skorohod [18], McKean [15], Bramso”
• Branching Brownian motion seen from its tip (2011, methodology): “Kyprianou in the context of branching Brownian motion to study traveling wave solutions to the F-KPP equation [22].”
• Further probabilistic analysis of the Fisher–Kolmogorov–Petrovskii–Piscounov equation: one sided travelling-waves (2006, methodology): “See McKean [31,32] and Neveu [33], whilst Kyprianou [27] and Harris [18] give complete expositions that are also particularly relevant for the techniques used in this paper.”